Solve ax² + bx + c = 0 for x, including complex roots — free and instant.
Enter the three coefficients of a quadratic equation in the standard form ax² + bx + c = 0, and this solves for x using the quadratic formula: x = (-b ± √(b² - 4ac)) / 2a.
The discriminant (b² - 4ac) determines what kind of roots the equation has. A positive discriminant gives two distinct real roots; exactly zero gives one repeated real root; a negative discriminant means the equation has no real solutions at all, only a pair of complex roots — shown here in the standard a ± bi form rather than treated as an error, since that's the mathematically correct answer.
When A, B, and C are whole numbers and the equation has real roots, this also shows the factored form using the "split the middle term" method: find two numbers that multiply to give a×c and add to give b, rewrite the middle term as the sum of those two, then factor by grouping. This only produces a clean result when the roots are rational — if they involve a square root or are complex, the factored form is skipped rather than shown incorrectly.
That happens when the discriminant (b² - 4ac) is negative — the equation still has a solution, just not a real number. This tool shows the complex roots in a ± bi form rather than reporting an error.
No — if A is 0, the equation isn’t quadratic anymore (it becomes linear), and this tool will tell you that directly rather than attempt to solve it.
Factoring by splitting the middle term only works cleanly when the roots are rational (whole numbers or simple fractions) — if the roots involve a square root or are complex, there’s no clean integer factorization to show, so this tool omits it rather than display something incorrect.
No — the calculation happens entirely in your browser.